[N,k,chi] = [836,2,Mod(1,836)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(836, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("836.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(2\)
\(-1\)
\(11\)
\(1\)
\(19\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{6} - T_{3}^{5} - 17T_{3}^{4} + 13T_{3}^{3} + 69T_{3}^{2} - 21T_{3} - 30 \)
T3^6 - T3^5 - 17*T3^4 + 13*T3^3 + 69*T3^2 - 21*T3 - 30
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(836))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( T^{6} - T^{5} - 17 T^{4} + 13 T^{3} + \cdots - 30 \)
T^6 - T^5 - 17*T^4 + 13*T^3 + 69*T^2 - 21*T - 30
$5$
\( T^{6} - 5 T^{5} - 9 T^{4} + 77 T^{3} + \cdots + 18 \)
T^6 - 5*T^5 - 9*T^4 + 77*T^3 - 99*T^2 + 9*T + 18
$7$
\( T^{6} + 2 T^{5} - 25 T^{4} - 58 T^{3} + \cdots - 96 \)
T^6 + 2*T^5 - 25*T^4 - 58*T^3 + 81*T^2 + 156*T - 96
$11$
\( (T + 1)^{6} \)
(T + 1)^6
$13$
\( T^{6} - 8 T^{5} - 23 T^{4} + 246 T^{3} + \cdots - 40 \)
T^6 - 8*T^5 - 23*T^4 + 246*T^3 - 191*T^2 - 254*T - 40
$17$
\( T^{6} + 2 T^{5} - 72 T^{4} - 48 T^{3} + \cdots - 256 \)
T^6 + 2*T^5 - 72*T^4 - 48*T^3 + 1168*T^2 - 1248*T - 256
$19$
\( (T + 1)^{6} \)
(T + 1)^6
$23$
\( T^{6} - 5 T^{5} - 88 T^{4} + \cdots - 7232 \)
T^6 - 5*T^5 - 88*T^4 + 332*T^3 + 2128*T^2 - 5008*T - 7232
$29$
\( T^{6} - 10 T^{5} - 91 T^{4} + \cdots - 11424 \)
T^6 - 10*T^5 - 91*T^4 + 1028*T^3 + 513*T^2 - 13890*T - 11424
$31$
\( T^{6} - 3 T^{5} - 79 T^{4} + 387 T^{3} + \cdots - 142 \)
T^6 - 3*T^5 - 79*T^4 + 387*T^3 - 201*T^2 - 697*T - 142
$37$
\( T^{6} - 7 T^{5} - 110 T^{4} + \cdots - 5856 \)
T^6 - 7*T^5 - 110*T^4 + 328*T^3 + 3936*T^2 + 4944*T - 5856
$41$
\( T^{6} - 6 T^{5} - 43 T^{4} + 464 T^{3} + \cdots - 896 \)
T^6 - 6*T^5 - 43*T^4 + 464*T^3 - 1479*T^2 + 1964*T - 896
$43$
\( T^{6} - 16 T^{5} - 49 T^{4} + \cdots + 39880 \)
T^6 - 16*T^5 - 49*T^4 + 1516*T^3 - 1235*T^2 - 34334*T + 39880
$47$
\( T^{6} - 124 T^{4} + 176 T^{3} + \cdots + 10752 \)
T^6 - 124*T^4 + 176*T^3 + 3216*T^2 - 11712*T + 10752
$53$
\( T^{6} - 20 T^{5} + 52 T^{4} + \cdots + 32960 \)
T^6 - 20*T^5 + 52*T^4 + 864*T^3 - 3344*T^2 - 10304*T + 32960
$59$
\( T^{6} - 15 T^{5} - 106 T^{4} + \cdots - 28064 \)
T^6 - 15*T^5 - 106*T^4 + 1396*T^3 + 4680*T^2 - 16976*T - 28064
$61$
\( T^{6} - 24 T^{5} + 60 T^{4} + \cdots + 25152 \)
T^6 - 24*T^5 + 60*T^4 + 1696*T^3 - 7440*T^2 - 18432*T + 25152
$67$
\( T^{6} - 25 T^{5} + 77 T^{4} + \cdots - 56022 \)
T^6 - 25*T^5 + 77*T^4 + 2429*T^3 - 22689*T^2 + 63345*T - 56022
$71$
\( T^{6} + 9 T^{5} - 157 T^{4} + \cdots - 82154 \)
T^6 + 9*T^5 - 157*T^4 - 1333*T^3 + 4881*T^2 + 29669*T - 82154
$73$
\( T^{6} + 26 T^{5} + 20 T^{4} + \cdots + 60672 \)
T^6 + 26*T^5 + 20*T^4 - 3016*T^3 - 10512*T^2 + 35616*T + 60672
$79$
\( T^{6} + 16 T^{5} - 20 T^{4} + \cdots - 4096 \)
T^6 + 16*T^5 - 20*T^4 - 1056*T^3 - 4784*T^2 - 7808*T - 4096
$83$
\( T^{6} + 2 T^{5} - 77 T^{4} + \cdots - 7968 \)
T^6 + 2*T^5 - 77*T^4 - 86*T^3 + 1545*T^2 + 1068*T - 7968
$89$
\( T^{6} - 7 T^{5} - 226 T^{4} + \cdots + 1152 \)
T^6 - 7*T^5 - 226*T^4 + 1184*T^3 + 4752*T^2 - 20736*T + 1152
$97$
\( T^{6} - 37 T^{5} + 334 T^{4} + \cdots + 405664 \)
T^6 - 37*T^5 + 334*T^4 + 1364*T^3 - 24472*T^2 + 3760*T + 405664
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